Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
242 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #11745302 |
| commutator, cosocle | C42×C29 | C23 |
| Frattini | C42 | C22×D29 |
| Fitting | C29×#486 | C2 |
| socle | C22×C29 | #127 |
| hypercenter | #486 | D29 |
| hypocenter | C29 | #1721 |
| LCS | G ▷ C42×C29 ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #486 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271540 | C2 | semidirect |
| 2. #14271539 | C2 | semidirect |
| 3. #14271539 | C2 | semidirect |
| 4. #14271537 | C2 | semidirect |
| 5. #14271511 | C2 | semidirect |
| 6. #14270885 | C2 | semidirect |
| 7. C29×#486 | C2 | semidirect |
| 60. #6597 | D8 | semidirect |
| 81. #486 | D29 | semidirect |
| 102. C29 | #1721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271540 | 2 |
| #14271539 | 2 |
| #14271537 | 2 |
| #14271511 | 2 |
| #14270885 | 2 |
| C29×#486 | 2 |
| #1721 | 29 |